http://www.straightdope.com/classics/a1_110.html
Just for clarification: the actual purpose of the scroll ‘s’ (also called the long s, latin s, or medial s) was to save space. As with the various typesetting ligatures to hit the scenes later, any s that was not either upper case, or at the end of a word was replaced with the slimmer more accomodating medial s.
Parchment and scribes weren’t cheap!
If that’s so, then why didn’t the scribes use the long s at the end of words? It would have been equally space-saving.
Because in handwritten forms, it’s slanted (like /), and is shaped like an integral sign. (In fact, that’s what the integral sign is. At the end of a word, that looks crufty.
Well, don’t people normally look at the beginning and end of words when reading? Maybe drawing it out distinctly at the end made things clearer.
Also, why would we use S as the integral sign?
Same reason as we use a capital sigma for series: it denotes summation.